Gradient-based control and optimization of boundary layer transition

In flow past bodies, small amounts of surface suction can delay the transit ion from laminar to turbulent flow. Suction therefore has significant poten tial to reduce the drag and hence the operating costs of aircraft. To obtai n best results the suction distribution must be optimized, and, if necessar y, should be adjusted to take account of changing conditions. Here distribu ted suction is used through a number of independently controlled discrete s uction panels, with transition maintained at a desired location while an au tomatic adaptive control feedback loop regulates the suction flowrates. The combination of minimum suction effort with constant transition position is expressed as a constrained optimization problem. A gradient-based algorith m is used to perform the control and optimization. Up to six suction panels are used, and flows both with and without an imposed pressure gradient are considered. In simple cases the method converges rapidly, but in other sit uations there is no single optimum solution within the numerical tolerance of the method. There are also cases in which an optimum solution exists but cannot be achieved as it occurs at a discontinuity in the relationship bet ween the transition position and the suction flowrates. Similar problems co uld occur with other cost functions and formulations, and when using differ ent solution algorithms.